● Covered by 1 source · 1 reportLow impact1 neutral
AI Used to Generate Lean Proof for Conway's Refinement Conjecture
Key points
- A user generated a Lean proof for Conway's Refinement Conjecture.
- The proof was created using an AI model over a month.
- It passed mechanical checks and received preliminary positive feedback.
- Independent mathematical verification is still pending.
AI-Assisted Proof Generation
A user reports generating a Lean proof for John Conway's Refinement Conjecture. This effort involved using an AI model over approximately one month, consuming a significant amount of computational tokens. The user, who self-identifies as a 'math noob', aimed to explore the capability of frontier AI models in solving open mathematical problems.
Conway's Refinement Conjecture
The conjecture, posed by John Conway 50 years ago, states that omnific integers possess a refinement property. Specifically, if ab = cd, then there exist integers e, f, g, h such that a = ef, b = gh, c = eg, and d = fh. This property relates to the factorization of integers.
Verification Status
The generated proof has not yet undergone independent verification by mathematicians. However, it has successfully passed mechanical checks from the Palomar registry. Additionally, individuals familiar with both the Lean proof assistant and the relevant mathematical field have indicated that the statement appears correct. The user invites refutation of the proof.
Motivation and Approach
The user was motivated by recent headlines regarding AI math results and the meme 'Do a breakthrough'. The goal was to find an open mathematical problem and use an AI model to solve it, despite not fully understanding the problem's substance. The problem was selected after asking Claude to suggest an open problem in the field of surreal numbers, another invention of John Conway.
✨ This summary was generated by AI from the outlets' reporting listed below. It is not independently verified and may contain errors — check the original sources. How BrevFeed works →
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Primary sources
GitHub gaearon/analysis-solutions GitHub gaearon/conway-refinement GitHub leanprover-community/mathlib4 GitHub leanprover/comparator GitHub cameronfreer/lean4-skills GitHub TauCetiProject/TauCetiReviewReporting from
A user claims to have generated a Lean proof for Conway's Refinement Conjecture using an AI model. The proof has passed mechanical checks and received positive feedback from some familiar with Lean and the field, though it awaits independent mathematical verification.